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OK, so if ~150 years ago some guy claimed the entire state of Delaware as his own and killed anyone who disagreed, and then passed that title on down to his heirs, his heirs would rightfully own the entire state of Delaware?

Why can't anyone legitimately dispute it? It's pretty easy to say "It looks as though your ancestor never properly homesteaded this property, so you have no claim to it, and therefore no right to exclude others from using it".

Why does it matter, in terms of having the moral right to control property, who recognizes such a moral right?

If someone can claim ownership of a parcel of land which then becomes private property, how come a large group of people can't can't claim ownership of a larger piece of land and regulate traffic on it?

That one?

Ownership over resources comes from homesteading those resources. Groups of people can only claim land that can be claimed by individual members of the group. If the individuals in the group have not homesteaded some land, then the group has no greater claim to that land than any other person in the world, and so the group can't just regulate traffic on it as if some member had homesteaded the land and then brought that into the group's ownership.

Private property is very much arbitrary if your method for deciding who owns private property is based on being given a title or deed by governments. Libertarians, however, believe that ownership of private property comes from homesteading unowned property; unowned resources become private property when the resources are mixed with the labor of some person.

National borders are much more arbitrary than this, because they are based entirely on some group of people claiming ownership over vast tracts and land and then killing anyone who stands up to them. They are not based on having any special relationship with the land, as homesteading requires, they are based on arbitrary claims backed up by having superior capability to bring about violence.